Geodesic
Higher order cohomology operations and minimal atomicity
Homology, homotopy, and applications, Tome 9 (2007) no. 1, pp. 1-43.

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We prove that $\Omega S^n_{(2)}$, $S^n\{2^r\}$, and $\Omega^2 S^n_{(2)}$ are minimal atomic spaces for appropriate values of $n$. We do this by using secondary and tertiary cohomology operations to prove that, above the Hurewicz dimension, no elements in the mod $2$ homology of the cited spaces are in the image of the Hurewicz homomorphism. In the case of $\Omega^2 S^n$, we construct and exploit an appropriate filtration to facilitate the use of higher order cohomology operations. An appendix consisting of an examination of the coefficients in Adams' factorization is included.
DOI : 10.4310/HHA.2007.v9.n1.a1
Classification : 55S20
Keywords: minimal atomic, cohomology operations 
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Rochelle Pereira. Higher order cohomology operations and minimal atomicity. Homology, homotopy, and applications, Tome 9 (2007) no. 1, pp. 1-43. doi : 10.4310/HHA.2007.v9.n1.a1. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2007.v9.n1.a1/

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